Solve graph values step by step from clues

3.MD.B.33.OA.A.3 · take · grade 3

Archetype: Solve a Table or Graph Step by Step from Clues · step in a 5-type progression

A class surveyed which season each student was born in and recorded the results in a picture graph. The number of students born in winter is $2$ times the number born in summer. Find the total number of students surveyed.

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $6$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $6$ circles, summer has $2$ circles, and autumn has $5$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times2=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

Understand

A picture graph shows students by birth season: spring 6, summer 2, autumn 5, and winter blank. The number born in winter is 2 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 6 students, summer = 2 students, autumn = 5 students (read from the graph).
Winter = 2 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the doubling rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

Execute

#1 Draw a Diagram 3.MD.B.3

The summer column has 2 circles, so 2 students were born in summer.

Counting a column's circles is direct picture-graph reading.

#7 Identify Subproblems 3.OA.A.3

Winter is 2 times summer: 2 × 2 = 4 students born in winter.

2 \times 2 = 4

'2 times' means double the summer count — a Grade 3 multiplication idea.

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 6 + 2 + 5 + 4 = 17 students.

6 + 2 + 5 + 4 = 17

The whole survey is just the sum of every season's count.

Answer: 17 students

Review

All season counts are small whole numbers (6, 2, 5, 4) and their sum 17 is a believable class size; winter (4) is indeed double summer (2), matching the rule.

Add the three known seasons first (6 + 2 + 5 = 13), then add winter (4) to get 13 + 4 = 17 — same total.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Doubling the summer count to find the winter count.

💡 This only needs Grade 3 'double it' multiplying and adding the columns — solve the knowable parts first!